A set of permutations is called sign-balanced if the set contains the same number of even permutations as odd permutations. Let $S_n(σ_1, σ_2, \ldots, σ_r)$ be the set of permutations in the symmetric group $S_n$ which avoids patterns $σ_1, σ_2, \ldots, σ_r$. The aim of this paper is to investigate when, for certain patterns $σ_1, σ_2, \ldots, σ_r$, $S_n(σ_1, σ_2, \ldots, σ_r)$ is sign-balanced for every integer $n>1$. We prove that for any $\{σ_1, σ_2, \ldots, σ_r\}\subseteq S_3$, if $\{σ_1, σ_2, \ldots, σ_r\}$ is sign-balanced except $\{132, 213, 231, 312\}$, then $S_n(σ_1, σ_2, \ldots, σ_r)$ is sign-balanced for every integer $n>1$. In addition, we give some results in the case of avoiding some patterns of length $4$.